| BTC (N = 2,081) | |
|---|---|
| Mean (sd) | 2,080; 0.22 ± 3.94 |
| median (Q1, Q3) | 2,080; 0.19 (-1.21, 1.78) |
| min | -37.16954 |
| max | 25.24717 |
| Cumulative Return | 466.6306 |
| Normally Distributed VaR | -6.25452002497649 |
| Non-Normally Distributed VaR | -6.05178991592173 |
The above statistics table is based on the percentage returns for the daily price valuation of bitcoin; it presents the mean, median, min, and max returns to demonstrate the range as well as the average return over the six year period from 2014 to 2020.
In regards to the mean return (%) of bitcoin, it can be noted that it is positive and relatively close in value to the median price meaning that over a daily basis, bitcoin is expected to provide approximately .22% return of an investment per day during a 6 year period. This can fluctuate depending on the valuation trend as the price of bitcoin can over a larger period be trending downwards, upwards or sideways. Given that the mean and the median are relatively close in value, there is limited skewness in the data, and the skewness is favoring higher returns since the mean is to the right of the median.
Colloquially, a bull market is defined as a financial securitity with a sustained increase in valuation; thus, a bear market is defined as a financial securitity with a sustained decrease in valuation; and a trendless market does not have either a sustained increase or a sustained decrease in valuation.
The standard deviation is approximately 3.94% which means that 95% of the daily returns will most likely fluctuate between [-7.66%, 8.01%]. Anything that occurs outside of this interval would be a rare event with a probability \(\le 5%\), which means that most of the returns would occur be centered around the mean, and 5% of the returns would be \([-\infty,-7.66\%]\cup[8.01\%,\infty]\) (outside of the interval [-7.66%, 8.01%]).
In addition, the minimum provided in this table is the greatest percent decrease in the valuation of bitcoin for a single day, and respectively, the maximum is the greatest percent increase in the valuation of bitcoin for a single day. While the cummulative return is the total percentage return over the full period of the investment.
Finally, the value at risk is approximately 6.25% which means that on a daily time frame, there is a probability of \(5\%\) that one could lose 6.25% on the daily, this is important information for trading and risks could be taken to mitigate the risks of a 6.25% drawback in one’s portfolio through hedging or other means.
There two figure presented above is a representation of the returns plotted against time which denotes the returns for each of the change in price valuation on the daily basis. In addition, the histogram represents the frequency for the returns within a .5% interval, and based on the graph there are some outlier in the distribution but it is mostly centered around the mean and it has a gaussian shape meaning that the returns are normally distributed. This can be tested using a form of normality test but will not given the visual shape of the data.
#Financial projections of Bitcoin: {.tabset}
## [1] 0.0003255208When simulating the data,
| BullMarket (N = 1,068) | |
|---|---|
| Mean (sd) | 0.49 ± 3.72 |
| median (Q1, Q3) | 0.27 (-0.78, 1.83) |
| min | -21.14486 |
| max | 25.24717 |
| Cumulative Return | 520.3815 |
| Normally Distributed VaR | -5.6378883280451 |
| Non-Normally Distributed VaR | -5.35477918110908 |
| BearMarket (N = 894) | |
|---|---|
| Mean (sd) | 0.01 ± 4.18 |
| median (Q1, Q3) | 0.10 (-1.66, 1.63) |
| min | -37.16954 |
| max | 18.18776 |
| Cumulative Return | 8.210591 |
| Normally Distributed VaR | -6.87117808582232 |
| Non-Normally Distributed VaR | -6.45995118699981 |
| FirstMinorBearMarket (N = 363) | |
|---|---|
| Mean (sd) | -0.40 ± 4.39 |
| median (Q1, Q3) | -0.01 (-2.38, 1.46) |
| min | -16.8548 |
| max | 14.78049 |
| Cumulative Return | -143.6408 |
| Normally Distributed VaR | -7.61358726528272 |
| Non-Normally Distributed VaR | -8.58836887321155 |
| FirstMinorBullMarket (N = 194) | |
|---|---|
| Mean (sd) | 0.78 ± 3.46 |
| median (Q1, Q3) | 0.32 (-0.63, 1.91) |
| min | -8.831367 |
| max | 17.35601 |
| Cumulative Return | 150.7003 |
| Normally Distributed VaR | -4.91756452906168 |
| Non-Normally Distributed VaR | -4.72327966403773 |
| SecondMinorBearMarket (N = 261) | |
|---|---|
| Mean (sd) | -0.23 ± 4.23 |
| median (Q1, Q3) | -0.21 (-1.79, 1.32) |
| min | -37.16954 |
| max | 15.57634 |
| Cumulative Return | -60.61308 |
| Normally Distributed VaR | -7.18986945691556 |
| Non-Normally Distributed VaR | -5.56762480911872 |
| SeconMinorBullMarket (N = 2,003) | |
|---|---|
| Mean (sd) | 2,002; 0.22 ± 3.82 |
| median (Q1, Q3) | 2,002; 0.19 (-1.21, 1.74) |
| min | -21.14486 |
| max | 25.24717 |
| Cumulative Return | 431.644 |
| Normally Distributed VaR | -6.07594799566695 |
| Non-Normally Distributed VaR | -6.04638976371344 |
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 27.8 2978.1 9921.5 45473.0 30992.1 3081023.7## 5% 10% 15% 20% 25% 30%
## 641.5792 1064.0722 1586.3620 2176.9280 2978.0662 3973.6076
## 35% 40% 45% 50% 55% 60%
## 5155.1599 6341.4031 8186.7371 9921.5147 12009.6031 15296.2046
## 65% 70% 75% 80% 85% 90%
## 19908.2748 23702.6301 30992.0557 41590.4879 58419.2534 88290.1358
## 95% 100%
## 153157.3189 3081023.7194